In this paper, a multiple-input multiple-output wiretap channel model is studied, where the information packet sent from the transmitter to the desired receiver is wiretapped by a potential eavesdropper. When ideal channel state information (CSI) is available, we design the secure beamforming using a proposed iterative closed-form updating scheme based on majorization-minimization approach. Numerical results demonstrate that the proposed scheme acquires the same secrecy rate as the existing algorithms whereas it has much lower complexity. When ideal CSI is not available and channel errors are modeled by deterministically bounded model, we investigate robust secure beamforming (RSB) optimization problem whose goal is worst-case secrecy rate maximization. In the formulated optimization problem, the objective function includes the expression of a logarithm of a determinant (log det) minus log det. Instead of approximating the log det expression as a trace, we propose to linearize two log det terms. After linearization, epigraph reformulation is used to deal with deterministically bounded channel errors and semi-infinite constraints are recast as linear matrix inequalities. Finally, an alternating optimization algorithm is utilized to find the RSB design. After obtaining the RSB design, we derive the worst-case secrecy rate. Numerical results illustrate that the proposed RSB design is superior to the nonrobust one.